Are there any spoilers about how and why she was able to see into the future?

WWait what? No she can't see into the future. She was reincarnated. Did u skip the beginning?

she wasnt reincarnated , she saw her future in her dream

apparently it was a magical tool(can't remember what exactly was it: a necklace?) that enabled her to see her future(?) in the novel, they attributed it to the magical tool but it was never strongly confirmed. And Hugo mentioned that magical tools used to be normal but slowly disappeared over the years which is why you don't see any rn but apparently some noble families have kept magical tools including Hugos.

Lucia suspected that her visions were from a family heirloom of her mother's.

She was NOT reincarnated. Spoiler~
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She can see the future in her dream and this is caused by her family heirloom (which is a magical tool). And let me tell you, thank God she can see the future. If she couldn't and didn't do anything to change the future, we won't be able to see happy Lucia, happy Hugo, happy Damian, happy little girl, and a peaceful kingdom. In short, the future of the world she's living in would have been a terribly dark and cold one. If you read the novel, I'm sure you'd cry